Introductory remarks / K. Mahler -- Minkowski's theorem on successive minima / P. T. Bateman -- Reduction of a complex body / K. G. Ramanathan--The Minkowski- Hlawka theorem / A. Dvoretzky -- Roger's theorem on successive minima / K. Mahler -- A mean value theorem / P. T. Bateman -- Non-homogeneous lattices in two dimensions / A. M. Macbeath.